In this project Least Square Estimator (LSE) to classify images.
Linear Regression Model:
A regression model relates a dependent (response) variable y to a set of k independent explanatory variables {x1, x2 ,…, xk} using a function. When the relationship is not exact, an error term e is introduced.
y=f(x1,x2,….,xk)+e (1)
If the function f is not a linear function, the above model is referred as Non-Linear Regression Model. If f is linear, equation (1) is expressed as linear combination of independent variables xk weighted by unknown vector parameters θ = {θ1, θ2,…, θk } that we wish to estimate.
y=x1θ1+x2θ2+⋯+xkθk+e (2)
Equation (2) is referred as Linear Regression model. When N such observations are made
y=x1iθ1+x2iθ2+⋯+xkiθk+e,(i=1,2,…,N) (3)
Then convenient to express all the variables in matrix form when N observations are made.
And finally denoting equation (3) using (4)
y=Xθ+e
